Question

Fig.8-18 3.30 Show that 3t5 +108 4 15t +1 is an allowable change of parameter for all t. 3.31 Find an allowable change of parameter which maps the interval 0<t2 onto 00. 3.32 Compute the length of the are x= et(cos t)e, + et(sin t)eg + eteg, 0 t T. Ans. 3(e-1) Referring to Problem 8.28, find are length as a function of e along the hypocycloid. 3.33. (TO-r) cos e +r cos (ro-r) sine r sin To> r 4r(ro 1-cos (r-e/2r)l Ans. s

pls do 3.30,3.31, and 3.32
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Answer 1

0 = 3 4 + 1 ot tist+1, do = 15 + + 30t2 +15 do = 15 [ + +2 +² + 1] do = 15 (+2+1)? do to , for all it (: (t + 1)²²0) o is an allowable change of parameter t at OSAST S 3testo do = 15 (+4+24² + 1) & Loco = 3t5 tlat + ist +120 xht) = et costje, to tesint) ez tetez, dx = (etc-sit) + Costiet) e 1 + (et cost+ sintetlen tete S" 1 1 4 * $ et sit )? ce test.j = [(cost-sint). et J² + [(cast tsikt). el/ 2 + ²t det 1=1 et J 1 + 1 - 1 dt. s het ziet - B. [et]." = B [ "_e"] LA - J7 [-417